Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
n=int(input())
k=1
arr=[]
while (k*(k+1))//2<=n:
    arr.append((k*(k+1))//2)
    k+=1
start=0
end=len(arr)-1
flag=0
while start<=end:
    k=arr[start]+arr[end]
    if k<n:
        start+=1
        continue
    if k>n:
        end-=1
        continue
    else:
        flag=1
        break
if flag==1:
    print ('YES')
else:
    print ('NO')